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Prime Numbers and Representation Theory（素数与群表示论）
  • 书号：9787030533401
    作者：叶扬波,田野
  • 外文书名：
  • 装帧：平装
    开本：B5
  • 页数：
    字数：无
    语种：en
  • 出版社：科学出版社
    出版时间：1900-01-01
  • 所属分类：
  • 定价： ￥139.00元
    售价： ￥109.81元
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目录

  • Contents
    Preface
    The Average Number of Goldbach Representations Daniel A.Goldston Liyang Yang
    1. Introduction 1
    2. Results 3
    3. The Main Terms in the Asymptotic Expansion 3
    4. Gallagher's Lemma 6
    5. Bhowmik and Schlage-Puchta's Estimate 7
    6. Estimates for Primes on RH 8
    7. Proof of Theorems 1 and 2 9
    References 10
    Sieve Methods and Exponential Sums: An Interplay Between Combinatorics and Harmonic Analysis Angel V.Kumchev Introduction 13
    1. A Basic Example: The Distribution of p Modulo One 15
    1.1 First result.Vaughan's identity 15
    1.2 Preparation for the sieve 18
    1.3 A simple lower-bound sieve 22
    2. An Application to Additive Number Theory: Exceptional Sets for Sums of Squares of Primes 27
    2.1 A canonical application of the circle method 29
    2.2 Some background on quadratic exponential sums 32
    2.3 A first sieve result 35
    2.4 Zhao's major-arc idea 38
    2.5 A "full-scale" alternative sieve 41
    References 45
    Small Gaps Between Primes James Maynard
    1. Introduction-What are Sieve Methods, and What are They Good for? 48
    2. Small Gaps between Primes 51
    3. The Historical Path of Progress on Small Gaps 53
    4. The GPY Sieve Method 55
    5. How to Choose Weights wn? 56
    6. Proof of Main Theorem 58
    6.1 Reduction to quadratic forms 58
    6.2 Simplification of quadratic forms 61
    6.3 Reduction to smooth integrals 64
    6.4 Smooth optimization 67
    7. Explicit Gaps between Primes 70
    References 73
    Horizontal Non-Vanishing of Rankin-Selberg L-Values Ashay A.Burungale
    1. Introduction 76
    2. Generic Non-vanishing 78
    3. Non-vanishing I 80
    4. Non-vanishing II 84
    5. Epilogue 88
    References 90
    Eisenstein Series on the General Linear Group Joseph Hundley
    1. Lecture 1 94
    1.1 Some classical automorphic forms 94
    2. Lecture 2 102
    2.1 Basic definitions 103
    2.2 Adelic Eisenstein series connected with classical Eisenstein series 113
    3. Lecture 3 119
    3.1 Some notation 119
    3.2 Parabolic induction for GLn(Qp) 120
    3.3 Parabolic induction in the real case 127
    3.4 Matrix coe±cients 135
    3.5 Extension of polynomial functions 144
    3.6 Parabolic induction in the automorphic setting 146
    4. Lecture 4 148
    4.1 The exterior algebra of a vector space 148
    4.2 Using the exterior algebra to understand Bn(Q)nGLn(Q) 154
    4.3 On convergence of Eisenstein series 156
    4.4 Some aspects of the general theory 164
    References 171
    Two Main Conjectures in Langlands Program Yeansu Kim
    1. Notation and Preliminaries 174
    2. Local Langlands Correspondence 178
    2.1 Spherical case 178
    2.2 General linear groups case [22, 26, 56] 180
    2.3 L-functions from Langlands-Shahidi method 181
    3. Langlands Functoriality Conjecture 184
    3.1 Spherical (i.e.unramified) local functoriality 184
    3.2 Global Langlands functoriality conjecture 185
    3.3 Local functoriality: general case 185
    3.4 The descent method 186
    4. Recent Results 187
    4.1 Notation 187
    4.2 L-functions from Langlands-Shahidi method in the case of GSpin groups 188
    4.3 Classification of (strongly positive) discrete series representations of GSpin groups 189
    4.4 Construction of Langlands parameter 191
    4.5 Construction of L-packet 192
    4.6 Applications: two versions of generic Arthur packet conjectures for GSpin groups 193
    Acknowledgement 195
    References 196
    Local Factors, Reciprocity and Vinberg Monoids Freydoon Shahidi Introduction 200
    1. Artin Factors 203
    2. Local Langlands Correspondence for GL(n) (LLC) 204
    3. An Example: The Case of Exterior and Symmetric Square Factors for GL(n) 206
    4. The Proof 207
    5. Steps of the Proof 210
    6. Proof of (SCS) 213
    7. Cases of Exterior Cube for GLn 222
    8. The General Case 223
    9. Braverman-Kazhdan/Ngo Program 234
    References 253
    Local Aspects of the Langlands-Shahidi Method and the Theory of R-Groups David Goldberg Introduction 257
    1. Preliminaries and Notation 258
    1.1 Notation 258
    1.2 L-groups 259
    1.3 Parabolic subgroups 261
    1.4 Weyl groups 262
    2. Admissible Representations of G 262
    2.1 Basic definitions 262
    2.2 Matrix coe±cients 263
    2.3 Induced representations and classifications 263
    2.4 Intertwining operators 264
    3. Langlands Conjectures 268
    3.1 Framework 268
    3.2 Artin L-functions 268
    3.3 Parameterization conjecture 268
    3.4 Parameterization and induction 270
    3.5 Global conjecture 271
    4. Langlands Conjecture on Plancherel Measures 274
    5. Generic Representations 274
    5.1 Definitions 274
    5.2 Shahidi's local coe±cients and Plancherel measures 276
    6. Normalized and Self Intertwining Operators 278
    6.1 Existence of normalized operators 278
    6.2 Cocycle relation 278
    6.3 Rank one Plancherel measures 279
    6.4 Decomposition of intertwining operators 279
    6.5 Normalized operators span C(*) 281
    7. R-groups I 282
    7.1 Defining the R-group 282
    7.2 Cocycles and the commuting algebra 283
    8. R-Groups II-Dual Side R-Groups 284
    8.1 R-groups in the Langlands philosophy 284
    9. Examples 285
    10. State of the Conjectures 290
    10.1 Parameterization conjecture 290
    10.2 Functoriality conjecture 291
    11. Endoscopy and Twisted Endoscopy 291
    11.1 Twisted endoscopy 291
    12. Results for Inner Forms 296
    12.1 Parabolic subgroups of inner forms 297
    12.2 Local Jacquet-Langlands correspondence 297
    12.3 Transfer of Plancherel measures 298
    12.4 R-groups for inner forms of SLn 299
    12.5 Inner forms of quasi-split classical groups 299
    References 300
    Residues of Intertwining Operators for Sp(6): The Hyperbolic Term Vanishes Steven Spallone
    1. Introduction 308
    2. Preliminaries 309
    2.1 Notation 309
    2.2 Intertwining operators 309
    2.3 Definition of R(φG,φH,L) 310
    2.4 Elliptic terms 311
    3. Case of L = L0 312
    3.1 Weight factor for L a coset of pnL0 314
    3.2 Residue 316
    4. Appendix: Classic Harmonic Analysis Theorems 318
    References 320
    Index 322
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